Measuring Financial Cycles with a Model-Based Filter ...
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Measuring Financial Cycles with a Model-Based Filter:
Empirical Evidence for the United States and the Euro Area
Gabriele Galati∗, Irma Hindrayanto†, Siem Jan Koopman‡, Marente Vlekke§
∗ †De Nederlandsche Bank, The Netherlands‡VU University Amsterdam, The Netherlands
§Centraal Planbureau, Den Haag, The Netherlands
January 14, 2016
Abstract
The financial cycle captures systematic patterns in the financial system and is closely related
to the concept of procyclicality of systemic risk. This paper investigates the characteristics
of financial cycles using a multivariate model-based filter. We extract cycles using an un-
observed components time series model and applying state space methods. We estimate
financial cycles for the United States, Germany, France, Italy, Spain and the Netherlands,
using data from 1970 to 2014. For these countries, we find that the individual financial vari-
ables we examine have medium-term cycles which share a few common statistical properties.
We therefore refer to these cycles as ‘similar’. We find that overall financial cycles are longer
than business cycles and have a higher amplitude. Moreover, such behaviour varies over time
and across countries. Our results suggest that estimates of the financial cycle can be a useful
monitoring tool for policymakers as they may provide a broad indication about when risks
to financial stability increase, remain stable, or decrease.
Keywords: unobserved component models, state space method, maximum likelihood, band-
pass filter, short and medium term cycles.
∗Gabriele Galati, Economics and Research Division, De Nederlandsche Bank, The Netherlands.†Irma Hindrayanto, Economics and Research Division, De Nederlandsche Bank, The Netherlands.‡Siem Jan Koopman, Department of Econometrics, VU University Amsterdam, The Netherlands§Marente Vlekke, Centraal Planbureau, Den Haag, The Netherlands
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1 Introduction
This paper provides a new approach to measuring financial cycles, and examines their main
properties in the United States and the euro area1. The concept of financial cycles cap-
tures systematic patterns in the financial system that can have important macroeconomic
consequences, and is closely related to the concept of procyclicality of the financial system
(see e.g. Borio et al. (2001), Brunnermeier et al. (2009), and Adrian and Shin (2010)). The
financial cycle can be defined as self-reinforcing interactions between attitudes towards risk
and financing constraints, which translate into booms followed by busts (e.g. Borio (2014)).
The idea of financial cycles can be traced back to the writings of Fisher (1933), Kindleberger
(1978), Minsky (1986) and Minsky (1992).
The financial cycle plays an important role in the current policy debate on how to increase
the resilience of the financial system. Since the global financial crisis, policymakers have
increasingly re-oriented prudential policies towards a macroprudential perspective in an effort
to address the procyclicality of the financial system. The underlying idea is to build up buffers
during upswings in the financial cycle – booms in which imbalances build up – in order to be
able to draw them down during busts in which these imbalances unwind. The countercyclical
capital buffer in Basel III can be seen as an example of a policy instrument that responds to
the properties of the financial cycle, see Drehmann et al. (2011).
This re-orientation creates a need of accurately measuring the financial cycle. In recent
years, increasing research efforts have been made to respond to this need. Several methods to
measure the financial cycle have been proposed, which have helped gain a better understand-
ing of some key properties of the financial cycle. These methods include frequency-based or
‘non-parametric’ bandpass filters, and variations on the classic turning-point analysis algo-
rithm of Burns and Mitchell (1946). This line of research has arguably identified a financial
cycle that is best characterized by the co-movement of medium-term cycles in credit, the
credit-to-GDP ratio, and house prices. Peaks in this cycle tend to coincide with the onset of
financial crises.
In spite of these efforts, we are still far from thoroughly understanding the properties of
financial cycles comparable to our knowledge of the features of business cycles. This paper
contributes to reducing this gap by applying the Kalman filter to a multivariate unobserved
components time series model. In its most basic form, it decomposes a series into a long-term
trend and a short- or medium-term cycle. In a multivariate setting it can subsequently be
investigated whether the cycles of individual series have the same frequency and degree of
dependence on the past, in which case they are called ‘similar’ cycles.
This approach allows for diagnostic testing of the accuracy of the estimated trend and
cycle. Moreover, as opposed to non-parametric filters, it requires no prior assumptions on the
length of the cycle, which, given the exploratory stage of this research agenda, is particularly
convenient.
We apply our multivariate model-based filter to financial variables in the United States,
Germany, France, Italy, Spain and the Netherlands between 1970 and 2013. We analyze the
cyclical behavior of individual financial variables and attempt to identify the financial cycle
in terms of the behavior of a combination of variables. We also explore the time variation
1We thank Rene Bierdrager (DNB) for research assistance.
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in the characteristics of the financial cycle, which is important given the structural changes
in the financial landscape over the past three decades. We find three main results. First,
model-based filters allow to identify the cyclical behavior in house prices, credit and the
credit-to-GDP ratio. Second, we find evidence of substantial variation in the period and
amplitude of these cycles both over time and across countries. In particular, the amplitude
and duration of the financial cycles in the United States has increased since the mid-eighties,
consistent with the findings of Drehmann et al. (2012). We also find that in many cases
financial cycles are ‘similar’, as they have the same persistence, cycle length, spectrum and
cross-autocovariance funtion.
The remainder of this paper is organized as follows. Section 2 gives a brief overview of
the relevant literature on this topic. Section 3 discusses the modeling approach and Section
4 describes the data. Section 5 discusses the results for the United States and the five largest
economies in the euro area. Section 6 concludes.
2 Review of the Literature
The literature on measuring the financial cycle is still in its infancy, but has its roots in a
rich literature on systematic boom-bust patterns in the financial system that interact with
the macroeconomy. Early work includes the writings of Fisher (1933), Minsky (1986),Minsky
(1992) and Kindleberger (1978). In more recent times, two literature strands are relevant.
The first consists of empirical work on early warning indicators of financial stress (see
e.g. the surveys in Kaminsky et al. (1998), Demirguc-Kunt and Detragiache (2005) and
Chamon and Crowe (2012)). In the words of Shin (2013), this work is typically eclectic –
in the sense that it combines a variety of financial, real, institutional and political factors
– and pragmatic, i.e. it focuses is on goodness of fit rather than on providing theoretical
explanations of empirical facts. Only few attempts have been made at providing conceptual
underpinnings of early warning models (e.g. Shin (2013)).
The second related literature strand has documented how the dynamics of credit and
asset markets are linked to financial distress or macroeconomic activity (e.g. Borio and
Lowe (2002), Detken and Smets (2004), Goodhart and Hofmann (2008), Gerdesmeier et al.
(2010), Agnello and Schuknecht (2011); Alessi and Detken (2011), Edge and Meisenzahl
(2011), Schularick and Taylor (2012) and Taylor (2015)). Underlying this work is a view of
financial instability as an endogenous phenomenon that follows cyclical patterns. Excessively
strong growth in credit and asset prices reflects the build-up of financial imbalances that can
potentially unwind in a disruptive fashion with large negative macroeconomic consequences.
Until now, only few papers have tried to measure the financial cycle and investigate its
statistical properties. These papers rely mainly on three approaches: turning point analysis,
frequency-based filters and unobserved component time series models.
The first approach, turning point analysis, goes back to a long tradition of identifying
business cycles by dating their peaks and troughs, started by Burns and Mitchell (1946).
This is still used, most notably by the NBER and the Euro Area Business Cycle Dating
Committees. Claessens et al. (2011) and Claessens et al. (2012) are among the first to employ
this method to identify financial cycles for a large number of countries. They characterize
financial cycles in terms of peaks and troughs in three individual variables, namely credit,
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property prices and equity prices. They find that, compared to the business cycle, cycles in
these series tend to be more stretched out in time and more ample. They also present evidence
that credit and house price cycles – but not equity price cycles – are highly synchronized.
Moreover, they document that financial cycles and business cycles are closely linked.
The second approach uses statistical, frequency-based filters to identify the financial cycle.
The most well-known filters of this class are the Hodrick-Prescott filter and the bandpass
filters of Baxter and King (1999) and Christiano and Fitzgerald (2003). Such filters require
the user to pre-specify the range of cycle frequencies, which is why such filters are also referred
to as non-parametric filters. Aikman et al. (2015) use the bandpass filter of Christiano and
Fitzgerald to analyze the link between the credit cycle and the business cycle. The authors
estimate spectral densities of real and financial variables – real GDP growth, real bank loan
growth, real bank asset growth and real money aggregates – for a large set of countries
and over a long time period (1880-2008). The resulting spectral densities justify setting
a medium-term frequency range to extract financial cycles. Their evidence points to the
existence of a credit cycle with similar characteristics to that documented by turning point
analyses. They also show that credit booms tend to be followed by banking crises.
A few papers apply both approaches, in an attempt to reach more robust conclusions. For
example, Igan et al. (2009) use the bandpass filter of Corbae and Ouliaris (2006) to filtered
the data, and then feed the results into a generalized dynamic factor model. Thereafter, they
use the turning point analysis to identify the duration and amplitude of cycles in house prices,
credit and real activity. Their results reveal that real and financial cycles have attained more
common characteristics over time, which they attribute to growing financial integration.
In an influential paper, Drehmann et al. (2012) combine turning-point analysis and the
bandpass filter by Christiano and Fitzgerald (2003). They apply both methods to five fi-
nancial variables – credit, the credit-to-GDP ratio, property prices, equity prices and an
aggregate asset price index, which combines property and equity prices – to a set of indus-
trial countries over the period 1960-2011. Drehmann et al. (2012) distinguish short-term
cycles, which like business cycles last between 1 to 8 years, and medium-term cycles, which
last between 8 and 30 years. They thus identify the financial cycle as a medium-term phe-
nomenon with peaks tending to occur at the onset of financial crises, which have substantial
macroeconomic effects.
A third approach applies the Kalman filter to unobserved components time series models
to extract cycles (see Harvey (1989) and Durbin and Koopman (2012) for an overview). This
approach has been applied extensively to business cycle analysis (see e.g. Valle e Azevedo
et al. (2006), Koopman and Azevedo (2008) and Creal et al. (2010)). Koopman and Lucas
(2005) are among the few who provide an application to financial variables. They extract
cycles from credit spreads, business failure rates, and real GDP in the Unites States and find
evidence of comparable medium-term cycles.
Compared to the non-parametric bandpass filters applied in most other research on this
topic, model-based filters have a number of advantages. First, rather than imposing ad-
hoc parameters on the Kalman filter, these parameters are model driven, in particular they
are derived from estimating an unobserved component model with a maximum likelihood
method. Second, since the filter is based on a model, researchers have the possibility to
use diagnostics to estimate the fit and validity of this model and hence the accuracy of
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their estimates. Third, whereas non-parametric filters and turning point methods require
predetermined frequencies to extract cycles, model-based filters estimate the cycle frequency.
This feature is especially convenient for the purpose of this research, since there is no broad
consensus yet on characteristics of financial cycles. Fourth, the Kalman filter can handle
non-normal data with ease, which is particularly useful for modeling financial data, which
notoriously have fat tails.
The literature on measuring financial cycles has highlighted three important methodolog-
ical issues. First, the jury is still out on what method is most reliable. Empirical studies
such as Igan et al. (2009), Drehmann et al. (2012), Hiebert et al. (2014) and Schuler et al.
(2015) in fact rely on both turning-point analysis and frequency-based filters.
Second, there is no consensus in the literature on which financial variables to include in
the analysis. Ideally, one would like to extract empirical regularities from long time series for
a large set of financial variables collected across a large set of countries. In practice, however,
data limitations constrain both the length of the time series, the geographic coverage and
the number of financial variables. Some studies concentrate on credit on the grounds that
it captures the essence of boom-bust cycles in the financial sector (e.g. Dell’Ariccia et al.
(2012), Jorda et al. (2014), Aikman et al. (2015), Taylor (2015)). Credit has also be seen
as a measure of financial flows that is conceptually comparable to the use of flows of goods
and services in the analysis of business cycles (Hiebert et al. (2014)). Among types of credit,
total credit has recently been shown as being particularly relevant for economies such as the
United States, where the bulk of credit to the private non-financial sector is not supplied by
banks, see Dembiermont et al. (2013). A variable commonly used in policy analysis is the
credit-to-GDP ratio. The deviation of this variable from its long-term trend, called ”credit-
to-GDP gap” has been found to be a good early warning indicator for banking crisis, e.g.
Borio and Lowe (2002). It has also recently been introduced in the regulatory framework
under Basel III, see Edge and Meisenzahl (2011) and Drehmann and Tsatsaronis (2014).
More often, researchers have looked at measures of credit and asset prices, most notably
real estate prices (see for example Claessens et al. (2011) and Claessens et al. (2012)). In
Drehmann et al. (2012), credit aggregates (and in particular the credit-to-GDP ratio) are
used as a proxy for leverage, while property prices are used as a measure of available collateral.
Recent research also highlighted the usefulness of the debt-to-service ratio, see Drehmann
and Juselius (2012). Other financial variables that capture the attitude towards risk and
stress in the financial sector, e.g. credit spreads, risk premia and default rates, are seen as
providing useful complementary information (BIS, 2014).
Third, there is no consensus on how to combine multiple variables into one single measure
of financial cycle, as illustrated in the debate on date-then-average and average-then-date
approaches in the business cycle literature in Stock and Watson (2014). Three alternative
approaches have been used. The first consists of estimating cycles of individual financial
variables and then taking averages, see Drehmann et al. (2012) and Schuler et al. (2015).
A second approach is used by Hiebert et al. (2014) extracts cycle measures from individual
time series and then aggregates these estimated cycles using principal component analysis. A
third approach is used by Koopman and Lucas (2005), who construct a multivariate model of
different financial variables and then test formally whether the individual cycles are similar
to each other.
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3 Modeling Approach
In our empirical analysis, we proceed in two steps. First we follow Koopman and Lucas
(2005) and apply the Kalman filter to extract cycles from a set of financial time series for the
United States and five euro area countries. Second, we formally test whether these cycles
share a few important statistical properties, in an effort to establish common characteristics.
If we find evidence of some common characteristics in financial cycles, we refer to these as
‘similar’ cycles.
3.1 Unobserved Components Time Series Models
Suppose the number of time series under scrutiny is equal to p. Let yt denote a vector that
contains the values of p time series at time t, for t = 1,...,n. Then, in its most basic form,
an unobserved components model is formulated as the following trend-cycle decomposition:
yit = µit + ψit + εit, εiti.i.d.∼ N (0, σ2
ε,i), i = 1, . . . , p, (1)
where yit denotes the value of the ith element of yt at time t, µit is a long-term trend and ψit
is equal to a variable representing short- to medium-term cyclical dynamics. The residuals
εit are assumed to to be normally distributed and independent from εjs, for i 6= j and t 6= s.
All these components are unobserved and therefore need to be estimated via the Kalman
filter.
There are two crucial challenges in the decomposition of yt. The first is to choose how
smooth the trend should be, i.e. how much fluctuation in the variable is assigned to the
trend as opposed to the cycle. Our approach can be illustrated by defining in a general form
the mth-order trend for series i as, following Harvey and Trimbur (2003),
µ(m)i,t+1 = µ
(m)it + µ
(m−1)it ,
µ(m−1)i,t+1 = µ
(m−1)it + µ
(m−2)it ,
...
µ(1)i,t+1 = µ
(1)it + ζit, ζit
i.i.d.∼ N (0, σ2ζ,i),
(2)
meaning that ∆mµ(m)i,t+1 = ζit.
The smoothness of the trend depends on the differencing order m. In the frequency
domain a higher value for m implies that the low-pass gain function will have a sharper
cutoff. As m increases, the resulting trend therefore becomes smoother. If m = 0, it is
assumed that yt is already stationary. If m = 1, yt has a random walk process as the trend.
If m = 2, yt is specified as an integrated random walk,
µi,t+1 = µit + βit,
βi,t+1 = βit + ζit, ζiti.i.d.∼ N (0, σ2
ζ,i).(3)
For most macro economic time series the maximum order for m is set to 2, see for example
Valle e Azevedo et al. (2006). This specification has also used for financial variables, for
example by Koopman and Lucas (2005) who model GDP, business failure rates and credit
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spreads in a multivariate setting.
The second crucial challenge is to specify an appropriate stochastic process for the cycle
ψit. We follow the standard approach by Harvey (1989) and model the cycle as an autore-
gressive process of order 2, of which the polynomial autoregressive coefficients have complex
roots. Accordingly, ψit is specified as a trigonometric process, given by(ψi,t+1
ψ∗i,t+1
)= φi
[cosλi sinλi
− sinλi cosλi
] (ψit
ψ∗it
)+
(ωit
ω∗it
),
(ωit
ω∗it
)i.i.d.∼ N (0, σ2
ω,i), (4)
with frequency λi measured in radians, 0 ≤ λi ≤ π, for i = 1,...,p. The period of the
stochastic cycle ψit is given by 2π/λi. φi is the persistence parameter or ‘damping factor’,
which we restrict to be 0 < φi < 1. This restriction on φi ensures that the cycle ψit is
modeled as a stationary stochastic process. The disturbances (ωit, ω∗it)′ are assumed to be
serially and mutually uncorrelated and normally distributed with mean zero and common
variance σ2ω,i.
3.2 Modeling Similar Cycles
The cycles in a panel of time series are termed similar if the frequency λi and persistence
parameter φi of each individual cycle are restricted to take the same values λ and φ, respec-
tively, such that(ψt+1
ψ∗t+1
)= φ
[cos (λ)Ip sin (λ)Ip
− sin (λ)Ip cos (λ)Ip
] (ψt
ψ∗t
)+
(ωt
ω∗t
), (5)(
ωt
ω∗t
)i.i.d.∼ N (0, I2 ⊗Σω)
where Ip denotes an identity matrix of order p and Σω is a diagonal p× p matrix. The p×1
vector ψt is equal to (ψ1t, ..., ψpt)′ and ψ∗t = (ψ∗1t, ..., ψ
∗pt)′. We use the likelihood ratio test
to check whether λi’s and φi’s are equal to λ and φ, respectively.
Note that if there is evidence of similar cycles, the extracted cycles in our panel have
three important common characteristics, namely the cycle frequency, spectrum and (cross)-
autocovariance function, and the degree of persistence, see Harvey and Koopman (1997).
We use the standard likelihood ratio test to check whether λi’s and φi’s are equal to λ and
φ respectively.
3.3 Estimation in state-space form
To estimate equations (1)-(5), we put them into the state space form
yt = Ztαt + εt, (6)
αt+1 = Ttαt + ηt, (7)
where equation (6) is referred to as the observation equation, while equation (7) is called
the state equation or the updating equation. The state vector αt contains the unobserved
trend and cycle. The system matrices Zt and Tt contain the parameters from equations
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(1) to (5). The state disturbance vector ηt contains the disturbances of the trend and cycle
equations. The Kalman filter recursions are applied to obtain filtered and smoothed estimates
of the unobserved components contained in αt. Maximum Likelihood is used to estimate the
unknown variances of the disturbances of the different unobserved components, as well as
the persistence parameter φi and the frequency parameters λi. For details of this estimation
method, see Schweppe (1965), Harvey (1989), and Durbin and Koopman (2012)2.
4 Data
To allow for comparisons between our results and the literature, we use credit, the credit-
to-GDP ratio and house prices to capture the financial cycle. We estimate our model with
both total credit and bank credit3. These variables are taken from the BIS macroeconomic
database, and are deflated by the CPI. All variables except the credit-to-GDP ratio’s are
expressed in logarithms. Our method can however be easily applied to other variables used
in recent research, such as leverage and the debt service burden, see Juselius and Drehmann
(2015).
We carry out our analysis for the United States, and the five largest economies of the
euro area, namely Germany, France, Italy, Spain and the Netherlands. Our sample period
for all countries except Italy is from 1970(1) to 2014(4), and is dictated by the availability
of the data on house prices that have recently been provided on the BIS website. The
sample period for Italy starts only from 1974(1) due to the availability of the credit data.
For multivariate estimation, data points at the start of a series that were unavailable for all
series were excluded.
5 Empirical Results
We find several interesting results. First, there is evidence of medium term financial cycles
in the United States and the euro area. In particular, the majority of estimated financial
cycles have lengths between 8 and 25 years, see Table 5.1. These lengths are significantly
longer than the typical length of the business cycle (between 6 and 8 years) as documented
in the literature.
Second, most of the financial cycles also have a larger amplitude compared to the business
cycle, as indicated by the range of the medium term fluctuations shown in Figures 5.1 and
Figures 5.2. More detailed results on the trend-cycle decompositions for different countries
are presented in Appendices A and B. The amplitude of the financial cycles ranges between
10% and 20%, while the typical business cycle amplitude found in the literature is around
5%, see Zarnowitz and Ozyildirim (2002).
Third, we find evidence of significant heterogeneity across countries. In particular, we
find marked differences between Germany and the Netherlands on the one hand, and France,
Italy and Spain on the other. Whereas the former has financial cycles of around 10 years,
2Computations are done by the library of state-space functions in SsfPack 3.0 developed by Koopman et al.(2008) for OxMetrics 8 by Doornik (2013).
3Detailed estimates using bank credit are not reported here, and are available upon request from the authors.
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the latter exhibits longer and larger financial cycles. This is consistent with the idea that
the financial sector in the euro area is not very homogeneous.
Fourth, we do not only observe heterogeneity across countries, but also over time. The
United States in particular has cycles which are much shorter and smaller in the pre-1985
period. This is consistent with research that documented how the financial cycle in the
United States have become much longer and more ample during the great moderation, see
Borio (2014).
Table 5.1: Main estimates of total credit, total credit-to-GDP ratio and house prices
US DE FR IT ES NL
Univariate cycles
φCR 0.998 0.946 0.986 0.994 0.998 0.984φC/GDP 0.994 0.982 0.977 0.991 0.998 0.963
φHPR 0.996 0.973 0.996 0.993 0.993 0.987period CR 14.56 7.78 12.13 17.53 13.08 10.27period C/GDP 15.50 24.75 16.84 16.94 15.99 11.77period HPR 14.41 10.11 15.08 12.35 14.51 10.41Log-likelihood 1754.2 1755.2 1681.1 1412.1 1495.7 1479.9AICc -3482.5 -3484.6 -3336.3 -2798.1 -2965.6 -2934.0BIC -3446.1 -3448.1 -3299.8 -2763.0 -2929.2 -2897.5
Similar cycles
φ 0.996 0.956 0.992 0.992 0.997 0.983period 14.61 9.78 14.66 14.67 14.31 10.53Log-likelihood 1753.5 1751.2 1677.4 1407.9 1494.3 1478.5AICc -3490.2 -3485.6 -3338.0 -2798.9 -2971.7 -2940.2BIC -3465.5 -3460.9 -3313.3 -2774.2 -2947.0 -2915.5
LR test 1.4 8.0 7.3 8.4 3.0 2.8AICc similar similar similar similar similar similarBIC similar similar similar similar similar similar
# observations 180 180 180 164 180 180
‘CR’ refers to total credit (real), ‘C/GDP’ refers to the total credit-to-GDP ratio and‘HPR’ refers to house prices (real). The estimated period of the cycle is in year. ‘LR’denotes the likelihood-ratio test statistic with H0 : λHP = λCR = λCR/GDP andφHP = φCR = φCR/GDP . The LR-test used in this application is asymptoticallyχ2-distributed with 4 degrees of freedom. Critical values of χ2(4) are 7.78, 9.49, and13.28 for 10%, 5% and 1% statistical significance level, respectively. ‘AICc’ denotes theAkaike Information Criterion with a correction for finite sample sizes. ‘BIC’ denotesthe Bayesian Information Criterion.
Fifth, we find evidence indicating that for most countries, the cycles of total credit, the
total credit-to-GDP ratio and house prices share a number of important characteristics.
These are the persistence of the cycles as measured by φ, the cycle lengths 2π/λ, and the
spectrum and (cross)-autocovariance functions. We refer to such cycles as ‘similar’ cycles.
For all countries in our sample, the LR tests, AICc and BIC indicate that imposing similar
cycles on total credit, the total credit-to-GDP ratio and house price cycles does not result in
a significantly smaller likelihood, implying that the more parsimonious similar cycles model
is a good fit.
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Figure 5.1: Overview univariate cycles for total credit, total credit-to-GDP ratio, and houseprices
Total Credit
1980 2000
-0.1
0.0
0.1
United StatesTotal Credit Total Credit-to-GDP
1980 2000
0.0
0.2 Total Credit-to-GDP House Price Index
1980 2000-0.25
0.00
0.25House Price Index
Total Credit
1980 2000
-0.025
0.000
0.025
0.050 GermanyTotal Credit Total Credit-to-GDP
1980 2000
0.0
0.1Total Credit-to-GDP House Price Index
1980 2000
-0.05
0.00
0.05House Price Index
Total Credit
1980 2000
-0.1
0.0
0.1 FranceTotal Credit Total Credit-to-GDP
1980 2000
0.0
0.1 Total Credit-to-GDP House Price Index
1980 2000
0.0
0.2 House Price Index
Total Credit
1980 2000
-0.1
0.0
0.1
0.2 ItalyTotal Credit Total Credit-to-GDP
1980 2000
0.0
0.1
Total Credit-to-GDP House Price Index
1980 2000
-0.2
0.0
0.2House Price Index
Total Credit
1980 2000
-0.1
0.0
0.1
0.2 SpainTotal Credit Total Credit-to-GDP
1980 2000
0.00
0.25Total Credit-to-GDP House Price Index
1980 2000
-0.25
0.00
0.25 House Price Index
Total Credit
1980 2000
0.0
0.1The Netherlands
Total Credit Total Credit-to-GDP
1980 2000
-0.1
0.0
0.1Total Credit-to-GDP House Price Index
1980 2000
0.0
0.2
House Price Index
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Figure 5.2: Overview similar cycles for total credit, total credit-to-GDP ratio, and house prices
Total Credit
1980 2000
-0.1
0.0
0.1
United StatesTotal Credit Total Credit-to-GDP
1980 2000
0.0
0.2 Total Credit-to-GDP House Price Index
1980 2000-0.25
0.00
0.25House Price Index
Total Credit
1980 2000
-0.025
0.000
0.025
0.050 GermanyTotal Credit Total Credit-to-GDP
1980 2000-0.05
0.00
0.05 Total Credit-to-GDP House Price Index
1980 2000
-0.05
0.00
0.05House Price Index
Total Credit
1980 2000
0.0
0.1France
Total Credit Total Credit-to-GDP
1980 2000
0.0
0.1 Total Credit-to-GDP House Price Index
1980 2000
0.0
0.2 House Price Index
Total Credit
1980 2000
-0.1
0.0
0.1
ItalyTotal Credit Total Credit-to-GDP
1980 2000
0.0
0.1
Total Credit-to-GDP House Price Index
1980 2000
-0.2
0.0
0.2House Price Index
Total Credit
1980 2000
-0.2
0.0
0.2 SpainTotal Credit Total Credit-to-GDP
1980 2000
-0.2
0.0
0.2Total Credit-to-GDP House Price Index
1980 2000
-0.25
0.00
0.25 House Price Index
Total Credit
1980 2000
0.0
0.1
The NetherlandsTotal Credit Total Credit-to-GDP
1980 2000
-0.1
0.0
0.1Total Credit-to-GDP House Price Index
1980 2000
0.0
0.2
House Price Index
11
Finally, we find that total credit and bank credit cycles co-move strongly in the euro
area, and have comparable length and amplitude. The same is true for the ratio of these
variables to GDP. By contrast, we find that in the United States, bank credit and total credit
cycles are subject to different dynamics. In particular, in the United States, the trend of
bank credit-to-GDP ratio is almost stationary, while total credit-to-GDP ratio exhibits an
upward trend. This result is consistent with the idea that in the United States markets play
an important role in financial intermediation. By contrast, in the euro area, most of credit
is supplied by banks.
6 Conclusions
In this paper we applied model-based filters to extract trend and financial cycles for the
United States and the euro area. Our analysis shows that credit, credit-to-GDP ratio and
real house prices exhibit overall medium-term cyclical behaviour with relatively ample fluc-
tuations. We also find that the period and amplitude of these cycles can vary over time and
differ per country. In particular, in the United States we found evidence that financial cycles
have increased in amplitude and duration since the mid-1980s. However, we cannot easily
detect such breaks in the euro area countries in our sample.
There are several issues which we plan to explore in future research. First, given that for
the countries in our sample we do find similar cycles, we plan to investigate the interactions
between these cycles and develop a possible aggregation measure. Second, it would be
interesting and straightforward to explore the robustness of our results to including other
financial variables, such as leverage and interest payment on debt. Third, tt would be useful
to apply our method to longer time series as collected for example by Jorda et al. (2014)
and Knoll et al. (2014). Fourth, it would also be interesting to explore the determinants of
cross-country variations of financial cycles in the euro area. Finally, our methodology can
be extended to studying the synchronicity of financial and business cycle.
12
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16
A Estimated components using univariate models for
total credit, total credit to GDP ratio, and house prices
Figure A.1: United States, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 2010
9
10Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
-0.1
0.0
0.1Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1.00
1.25
1.50
1.75Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
0.0
0.2 Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
4.5
5.0
5.5 Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010-0.25
0.00
0.25Cycle
17
Figure A.2: Germany, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 2010
7.0
7.5
8.0 Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
-0.025
0.000
0.025
0.050Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1.00
1.25Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
0.0
0.1Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
4.7
4.8
4.9
5.0Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010
-0.05
0.00
0.05Cycle
Figure A.3: France, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 2010
7
8Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
-0.1
0.0
0.1Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1.0
1.5
Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
0.0
0.1 Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
5.0
5.5Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010
0.0
0.2 Cycle
18
Figure A.4: Italy, 1974(1)-2014(4)
Log of Total Credit Trend
1980 1990 2000 2010
6.5
7.0
7.5Log of Total Credit Trend Cycle
1980 1990 2000 2010
-0.1
0.0
0.1
0.2Cycle
Total Credit-to-GDP Ratio Trend
1980 1990 2000 2010
0.75
1.25 Total Credit-to-GDP Ratio Trend Cycle
1980 1990 2000 2010
0.0
0.1
Cycle
Log of House Price Index Trend
1980 1990 2000 2010
4.75
5.00
5.25Log of House Price Index Trend Cycle
1980 1990 2000 2010
-0.2
0.0
0.2Cycle
Figure A.5: Spain, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 2010
6
7
Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
-0.1
0.0
0.1
0.2Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1.0
1.5
2.0Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
0.00
0.25Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
4.5
5.0
5.5
6.0Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010
-0.25
0.00
0.25 Cycle
19
Figure A.6: The Netherlands, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 20105
6
7Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
0.0
0.1 Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1
2
Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
-0.1
0.0
0.1Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
4.5
5.0
5.5Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010
0.0
0.2Cycle
B Estimated components using similar cycle models for
total credit, total credit to GDP ratio, and house prices
20
Figure B.1: United States, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 2010
9
10Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
-0.1
0.0
0.1Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1.00
1.25
1.50
1.75Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
0.0
0.2 Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
4.5
5.0
5.5 Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010-0.25
0.00
0.25Cycle
Figure B.2: Germany, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 2010
7.0
7.5
8.0 Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
-0.025
0.000
0.025
0.050Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1.00
1.25Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010-0.05
0.00
0.05 Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
4.7
4.8
4.9
5.0Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010
-0.05
0.00
0.05Cycle
21
Figure B.3: France, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 2010
7
8Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
0.0
0.1 Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1.0
1.5
Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
0.0
0.1 Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
5.0
5.5Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010
0.0
0.2 Cycle
Figure B.4: Italy, 1970(1)-2014(4)
Log of Total Credit Trend
1980 1990 2000 2010
6.5
7.0
7.5Log of Total Credit Trend Cycle
1980 1990 2000 2010
-0.1
0.0
0.1Cycle
Total Credit-to-GDP Ratio Trend
1980 1990 2000 2010
0.75
1.25 Total Credit-to-GDP Ratio Trend Cycle
1980 1990 2000 2010
0.0
0.1Cycle
Log of House Price Index Trend
1980 1990 2000 2010
4.75
5.00
5.25Log of House Price Index Trend Cycle
1980 1990 2000 2010
-0.2
0.0
0.2Cycle
22
Figure B.5: Spain, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 2010
6
7
Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
-0.2
0.0
0.2Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1.0
1.5
2.0Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
-0.2
0.0
0.2Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
4.5
5.0
5.5
6.0Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010
-0.25
0.00
0.25 Cycle
Figure B.6: The Netherlands, 1970(1)-2014(4)
Log of Total Credit Trend
1970 1980 1990 2000 20105
6
7Log of Total Credit Trend Cycle
1970 1980 1990 2000 2010
0.0
0.1 Cycle
Total Credit-to-GDP Ratio Trend
1970 1980 1990 2000 2010
1
2
Total Credit-to-GDP Ratio Trend Cycle
1970 1980 1990 2000 2010
-0.1
0.0
0.1Cycle
Log of House Price Index Trend
1970 1980 1990 2000 2010
4.5
5.0
5.5Log of House Price Index Trend Cycle
1970 1980 1990 2000 2010
0.0
0.2Cycle
23